Question

g you hang an object of mass m on a spring with spring constant k and find that it has a period of T. If you change the spring to one that has a spring constant of 2 k, the new period is

Answer 1

a) T = 2π
`\sqrt{(m)/(k) }`, b) T ’=
`(1)/(√(2) ) T`

Step-by-step explanation:

a) A system formed by a mass and a spring has a simple harmonic motion with angular velocity

w² = k / m

angular velocity and period are related

w = 2π /T

we substitute

4π²/ T² = k / m

T = 2π
`\sqrt{(m)/(k) }`

b) We change the spring for another with k ’= 2 k, let's find the period

T ’= 2π
`\sqrt{(m)/(k') }`

T ’= 2π
`\sqrt{ (m)/(2k) }`

T ’=
`(1)/(√(2) ) T`